Question

Examine the continuity of the function .

Answer 1

The given function is,

f( x )=2 x 2 −1

At x=3, the function becomes,

f( 3 )=2 ( 3 ) 2 −1 =17

The left hand limit of the function at x=3 is,

LHL= lim x→ 3 − f( x ) = lim x→ 3 − ( 2 x 2 −1 ) =17

The right hand limit of the function at x=3 is,

RHL= lim x→ 3 + f( x ) = lim x→ 3 + ( 2 x 2 −1 ) =17

It can be observed that, at x=3, LHL=RHL=f( 3 )=17.

Therefore, the function is continuous at x=3.